Scientific determinism

When I get into discussions of free will and intelligence and the nature of things, I often point out that the universe is deterministic. In its strictest form, determinism says that everything that will happen is as good as happened already, that everything is perfectly predictable. However, the type of determinism that I subscribe to is looser, and based on science. It is basically this:

Everything that occurs happens in accordance with strict rules.

Now, this doesn't say anything about predictability, and indeed we shall see that the predictability is far from perfect. However, I hold that my statement is a statement of determinism: everything is determined at a certain level of abstraction - nothing occurs that does not follow very definite patterns.

I will now proceed to throw three wrenches into the works and show how my statement defeats them.

1. Measurement problems
There are certain apparently nondeterministic processes, like the double pendulum. An arbitrarily small change in the initial conditions can cause a large change in the resulting motion. However, the process is actually deterministic - it is just that, to predict the motion, infinite precision of the initial conditions is needed, and this is physically impossible. It is a limitation in the measurement, not the process - the actual system follows very strict, deterministic rules. This applies to all related chaos theory-type problems.
The Heisenberg Uncertainty Principle may appear to come under this category as well, but that is based on a misconception.

2. Quantum probabilities
At the microscopic level, quantum mechanics is not all deterministic in the traditional sense. However, it still follows strict rules. The probabilities involved in quantum mechanics are well-defined. When you have a probability curve, it means that not all choices are equally likely. This is a form of determinism - there are clear constraints on the future. These probabilities exist for repeatable processes, so that it can be shown the probabilities exist. This is because all of quantum mechanics is based on equations that are defined as probabilities. It is our natural, innate understanding that predisposes us to expect determinism in a low-level form like classical mechanics and to think of quantum uncertainty as nondeterministic. It's not that there's only one way for a process to unfold, but there's only one way for a process to operate. Nonuniform probability distributions are a form of (weak) determinism.
The Heisenberg Uncertainty Principle falls under this category. It defines a limit not on measurement, but on state. For example, a particle constrained in position must have a certain uncertainty in its momentum, and this gives rise to higher lowest-energy states. Virtual particles are another example.

3. Stochastic processes
Stochastic processes, such as Brownian motion, are another source of randomness. They are truly random, as they are not based solely on initial conditions. However, they still do not weaken my statement of determinism, since all stochastic processes that exist are governed by equations describing the actions of its constituents that give rise to the random output. In general, they are also constrained by probability distributions, which as stated above is a form of determinism.

So the point is that the laws of physics constrain all that occurs in well-defined ways. This is the form of weak determinism I subscribe to, and from this many of my beliefs follow.

A short note: It could be argued, perhaps, that the probability inherent in so many physical processes is where god interacts with the world, or where the mind interacts with the brain. I would give this thought more weight if the output of the processes were uniformly random (that is, all values are equally likely), instead of having a distribution.